The present disclosure describes systems and techniques relating to time-varying notch filters.
Some signal processing circuits in a hardware system use integrated circuit (IC) dice of very small sizes, for example, 40 nano-meters (nm) and less. At such small dimensions of the component ICs, the signal processed by the circuit may suffer from greater interference due to other signals in the system. For example, a Bluetooth™ circuit in a hardware system with component ICs in the 40 nm range may be affected by various clock harmonics (also known as “spurs”) due to other signals in the system, such as a reference clock signal or other clock signals present in the hardware system. In this context, a harmonic or a spur is a component frequency of a signal that is an integer multiple of the fundamental signal frequency, i.e. if the fundamental signal frequency is f, the harmonics have frequencies 2f, 3f, 4f and so on.
The spurs may be produced at frequencies overlapping with the radio-frequency (RF) channels of the Bluetooth circuit discussed above, thereby affecting the sensitivity of the Bluetooth circuit. That is, due to the interference caused by the spurs in the Bluetooth RF channels, a Bluetooth signal packet received by the hardware system may not be decoded correctly by the Bluetooth circuit. For example, a clock signal external to the Bluetooth circuit may have a baseband frequency of 38.4 MHz. Accordingly, the 64th harmonic of the external clock signal has a frequency of 2457.6 MHz, which falls within the frequency range of the Bluetooth circuit (2402-2480 MHz). If the operating frequency of the Bluetooth circuit is set close to 2457 MHz, then the sensitivity of the Bluetooth circuit would be severely degraded due to the spur of the external clock signal.
In some systems, spurs in a signal processing circuit may be removed by using a linear time-invariant (LTI) notch filter. In this context, a notch filter is a signal processing device (implemented either in hardware or as software processes) that allows an input signal to pass through the device unaltered at most frequencies, but attenuates an input signal within a specific, narrow frequency range (which may be referred to as the bandwidth of the notch filter) to very low levels (referred to as the depth of the notch filter). For example, a notch filter with a center frequency of 2457 MHz may be used in the Bluetooth circuit described above to reduce the effect of the spur at 2457.6 MHz.
The frequency response of notch filter is characterized by its bandwidth and depth. The depth of the notch determines the level of the input signal power that is removed and accordingly the extent to which the sensitivity of the signal circuit is achieved, with notch filters of greater depth removing more interference power and achieving greater sensitivity of the signal circuit. The sensitivity of the signal circuit may be negatively affected due to a spur. The degradation in sensitivity is dependent on the power of the interfering spur interferer. For a spur having a large power, the degradation may be large enough to cause sensitivity of the signal circuit to fall below one or more requirements set forth in the Bluetooth standard. Most of this degradation may be avoided by an LTI notch filter of proper bandwidth and depth (prior art).
The bandwidth of the notch determines the frequency range over which the signal is attenuated or cancelled. For example, a notch filter with a center frequency of 2457 MHz and a bandwidth of 6 MHz would attenuate signals in the frequency range of 2457 MHz±3 MHz, i.e., 2454-2460 MHz.